Question

The measure of spt is b. The measure of tpr in s five more than two times spt. The measure of qps is twelve less than eight times the last measure of spt. Find the measure of spt, tpr, and qps.

Answer 1

Hello.

In your question, we can see that the points Q, P, and R can be assumed that they are in a straight line, meaning that the angle measures will add up to 180 (think of half a circle, which is 360 degrees).

This means that every angle added up will add up to 180 degrees.

Meaning we can set up the below equation:

$(8b-12)+(b)+(2b+5)=180$

$8b-12+b+2b+5=180$

$11b-7=180$

$11b=187$

$b=17$

After finding $b$, we can plug it back in to each expression for each angle measure.

∠QPS = $8b-12=8(17)-12=124$

∠SPT = $b=17$

∠TPR = $2b+5=2(17)+5=39$

Hope this helps!